ecture Outine Impeance Transformation Techniques Impeance-Amittance Conversion Matching with umpe Eements Stub Amittances an Shunt Matching Stub Impeances an Series Matching Doube Stub Matching Dr. W.J.R. Hoefer EEC 454 Microwave Engineering
Reasons for Impeance Transformation Maximum power is eivere when the oa an generator are matche to the ine. Proper input impeance transformation of sensitive receiver components (antenna, NA, etc.) improves the S/N ratio of the system. Impeance matching in a power istribution network (such as antenna array fee network) wi reuce ampitue an phase errors. Dr. W.J.R. Hoefer EEC 454 Microwave Engineering
Transforming Network Seection Criteria Compexity A simper impeance transformation network is usuay cheaper, more reiabe, an ess ossy than a more compex esign. Banwith arger BW increase in compexity. Impementation Short-circuite stubs in coax an waveguie. Open-circuite stubs in stripine an microstrip. Ajustabiity tuning screws in waveguies. Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 3
A ossess Matching Network Z o Matching Network oa Z Z o A ossess network matching an arbitrary oa impeance to a transmission ine. To avoi unnecessary power oss, matching network is ieay ossess. The impeance ooking in to the matching network is Z o. Refections are eiminate on the transmission ine to the eft of the matching network. There wi be mutipe refections between the matching network an the oa. Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 4
Matching with umpe Eements (a) jx (b) jx Z o jb Z Z o jb Z X ± B = R X Z X = + B R o Z o R Zo BR R + X Z R + X o B = ± X = ± ( Z R ) R o Z o R ( Zo R ) X section matching network. (a) Network for z insie the +jx circe (i.e. R >Z o ). (b) Network for z outsie the +jx circe (i.e. R <Z o ). Z must have non-zero rea part. D.M. Pozar, Microwave Engineering, n Eition, section 5., p.p. 5, John Wiey & Sons, 998 Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 5
Matching with umpe eements ( networks) Simpest type matching is -section with reactive eements Two possibe configurations: (a): network for z within +jx circe (b): network for z outsie +jx circe Reactive eements: capacitor or inuctor Parasitics imit usabe frequency range Soutions anaytica or using Smith Chart Dr. Y. Baeyens E438-Microwave Circuit Design.5 /5
Design an section matching network to match a series RC oa with an impeance Z = 00 - j 00 Ω, to a 00 Ω ine, at a frequency of 500 MHz. Soution: Step : Convert the oa impeance to amittance by rawing the SWR circe through the oa, an a straight ine from the oa through the center of the Smith Chart. Step : Move the oa impeance to the impeance circe of + jx (one in amittance Smith Chart) -- a j 0.3 in susceptance EEC344, Kevin Chen, HKUST
Step 3: Convert back to impeance. Step Step Step 3 Step 4 Step 4: Move to the center of the Smith Chart by aing an series inuctor EEC344, Kevin Chen, HKUST
Smith Chart Soution jx Z o jb Z Z =00 j00ω, Z o =00Ω, f o =500MHz. Pot z = j Draw SWR an y = circes Convert z to y A shunt susceptance to y Convert y to z A series reactance D.M. Pozar, Microwave Engineering, n Eition, Exampe 5., p.p. 54, John Wiey & Sons, 998 Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 6
Therefore we have b = 0.3, x =. (check this resut with the anaytic soution). Then for a frequency at f = 500 MHz, we have b C = = 0. 9 pf π fz 0 xz = 0 = 38. 8nH π f Is there another soution? EEC344, Kevin Chen, HKUST 3
Microwave Engineering January 9, 003 Smith Chart Soution jx jb Zo Z Z=00 j00ω, Zo=00Ω, fo=500mhz. Pot z = j Draw SWR an y = circes Convert z to y A shunt susceptance to y Convert y to z A series reactance D.M. Pozar, Microwave Engineering, n Eition, Exampe 5., p.p. 54, John Wiey & Sons, 998 Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 6 Smith Chart Soution jx Zo jb Z Z=00 j00ω, Zo=00Ω, fo=500mhz. Pot z = j Draw SWR an y = circes Convert z to y A shunt susceptance to y Convert y to z A series reactance D.M. Pozar, Microwave Engineering, n Eition, Exampe 5., p.p. 54, John Wiey & Sons, 998 Dr. W.J.R. Hoefer Dr. Wofgang J.R. Hoefer EEC 454 Microwave Engineering 7 4
Smith Chart Soutions & C Z o C Z Z o Z b = 0.3, x =. b = 0.7, x =. Y = jb Z = j = jx = jω byo b C = = = 0.9 pf B ω π fzo Zo = = = 46.nH xzo xzo = = = 38.8 nh ωb πfb ω π f Z = jx Y = j = jb= jωc X C = = =.6pF ωx πfxz o Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 8
There are two soutions for the matching networks. In this case, there is no substantia ifference in banwith between the two soutions. EEC344, Kevin Chen, HKUST 4
Singe Stub Matching Probems of Matching with umpe Eements: umpe eement impeance matching is not aways possibe or easiy reaizabe. Soutions: A section of open-circuite or short-circuite transmission ine (a stub ) connecte in parae or in series with the fee ine at a istance from the oa can be use. The tuning parameters are the istance from the oa () an the ength of the stub (). Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 9
Singe-stub matching shunt stub series stub Singe open or short circuite ength T (stub) connecte either in shunt or series at certain istance from oa No umpe components are require, convenient for MIC Shunt stub often preferre (especiay in stripine or µstrip) Parameters: istance series ine an vaue susceptance (or reactance) provie by shunt or series stub Shunt: choosen that after ine amittance into ine (Y) is Y 0 +jb, then stub susceptance = -jb; for series such that Z into ine has form Z 0 +jx Dr. Y. Baeyens E438-Microwave Circuit Design.5 3/5
Singe-stub tuning A singe open-circuite or short-circuite ength of transmission ine (i.e. a stub) can connect in either parae or series with the main fee ine to achieve impeance matching. -jb ( = Y 0 +jb @ the stub ) -jx ( = Z 0 +jx @ the stub ) The two ajustabe parameters are the istance,, from the oa to the stub position, an the vaue of susceptance or reactance provie by the shunt or series stub.
Singe-stub tuning Proper ength of both open or shore transmission ine can provie any esire vaue of reactance or susceptance. For a given susceptance or reactance, the ifference in engths of an open- or short-circuite stub is λ/4. For microstrip or stripine, open-circuite stubs are easier to fabricate. For ines ike coax or waveguie, however, short-circuite stubs are usuay preferre. (open-circuite stubs ten to raiate)
Shunt Stub Matching Y o Y o Y Open or shorte stub Y o Y = Z Matching Operations: Seect, so that y= +jb. Seect, so that the stub susceptance is jb. D.M. Pozar, Microwave Engineering, n Eition, Figure 5.4(a), p.p. 58, John Wiey & Sons, 998 Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 0
Singe-stub Shunt Matching For shunt stub in microstrip or stripine open stub is preferre (no VIA hoe neee), for waveguie, coax an aso to appy DC-bias short stub often more convenient? For Z =5+j0 Ω, esign two singe-stub shunt tuning networks to match oa to 50Ω ine (3 r E. book has ifferent exampe) First pot normaize oa impeance Convert to amittance by imaging Pot +jb circe on Y-chart (+jx on Z) Turn on SWR circe eas to two intersections (y & y ) Distance from oa to stub given by WTG scae Susceptance stub given by normaize amittance y & y ength stub for given b, etermine on Smith chart (start from short!). Dr. Y. Baeyens E438-Microwave Circuit Design.5 3/5
Microwave Engineering January 9, 003 Shunt Stub Matching Yo Yo Yo Y= Open or shorte stub Y Z Matching Operations: Seect, so that y= +jb. Seect, so that the stub susceptance is jb. D.M. Pozar, Microwave Engineering, n Eition, Figure 5.4(a), p.p. 58, John Wiey & Sons, 998 Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 0 Exampe 5. Soution Yo =0.47λ Yo Open or shorte stub Y= b=.33 Y Yo Z y=0 Z=5+j0Ω, Zo=50Ω, fo=ghz. Pot z =0.3+j0. Draw SWR an y = circes Convert z to y Transform y to y, =0.044λ A shunt susceptance to y The stub ength is: =0.47λ Dr. W.J.R. Hoefer Dr. Wofgang J.R. Hoefer EEC 454 Microwave Engineering b=.33 6
Exampe 5. Soution b=.33 Y o Y o Y Open or shorte stub Y o Y = Z y=0 Z =5+j0Ω, Z o =50Ω, f o =GHz. Pot z =0.3+j0. Draw SWR an y = circes Convert z to y Transform y to y, =0.387λ A shunt susceptance to y The stub ength is: =0.353λ =0.353λ b=.33 Dr. W.J.R. Hoefer EEC 454 Microwave Engineering
Singe-stub shunt matching on Smith Chart +jb circe Z z = 5 + = 0.3 + j0ω j0. = 0.38 0.84 = 0.044λ = 0.5 0.84 + 0.7 = 0.387λ y y = = + j.33 j.33 = 0.47λ = 0.353λ Dr. Y. Baeyens E438-Microwave Circuit Design.5 33/5
Two soutions singe-stub shunt matching Soution eaing to shortest ength transmission ines has ceary better banwith Shorter T reuce frequency variation match an aso in practice wi reuce osses Anaytica soution in book (p. 3-3) Dr. Y. Baeyens E438-Microwave Circuit Design.5 34/5
Singe-stub tuning Shunt stubs Smith chart For a oa impeance Z =60-j80, esign two singe-stub shunt tuning networks to match this oa to a 50Ω ine at GHz. z y =. j.6 = 0.3 + j0.4 -jb =+jb y y =+j.47 z y =-j.47 s.c. y y = 0.76 0.065 = 0.0λ = 0.35 0.065 = 0.60λ =.00 + j.47 =.00 j.47 = 0.095λ = 0.405λ
Singe-stub tuning At GHz, Z =60-j80 can be moee as a series combination of R=60Ω an C=0.995 pf. The frequency response is then = 0.0 λ = 0.60 λ = 0.095 λ = 0.405 λ
Microwave Engineering January 9, 003 Exampe 5. Soution Yo b=.33 Y Yo Yo Open or shorte stub Y= Z y=0 Z=5+j0Ω, Zo=50Ω, fo=ghz. Pot z =0.3+j0. Draw SWR an y = circes Convert z to y Transform y to y, =0.387λ A shunt susceptance to y =0.353λ The stub ength is: =0.353λ Dr. W.J.R. Hoefer b=.33 EEC 454 Microwave Engineering Series Stub Matching Zo Zo Zo Z= Open or shorte stub Z Y Matching Operations: Seect, so that z= +jx. Seect, so that the stub susceptance is jx. D.M. Pozar, Microwave Engineering, n Eition, Figure 5.4(b), p.p. 58, John Wiey & Sons, 998 Dr. W.J.R. Hoefer Dr. Wofgang J.R. Hoefer EEC 454 Microwave Engineering 3 7
Singe-stub Series Tuning? Match Z =00+j80 Ω to 50Ω ine using singe series opencircuit stub First pot normaize oa impeance Pot +jx circe on Z-chart Turn on SWR circe gives intersections (z & z ) Distance & from oa to stub given by WTG scae Reactance stub given by normaize impeance z & z ength stub for given b, etermine on Smith chart starting from open point on Z-chart. Dr. Y. Baeyens E438-Microwave Circuit Design.5 35/5
Exampe 5.3 Soution =0.397λ b=.33 Z o Z o Z Z o Z = Y Open or shorte stub Z =00+j80Ω, Z o =50Ω, f o =GHz. Pot z =+j.6 Draw SWR an z = circes Transform z to z, =0.0λ z= A series reactance to z The stub ength is: =0.397λ b=.33 Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 4
Microwave Engineering January 9, 003 Exampe 5.3 Soution Zo =0.397λ Zo Zo Z= b=.33 Z Y Open or shorte stub z= Z=00+j80Ω, Zo=50Ω, fo=ghz. Pot z =+j.6 Draw SWR an z = circes Transform z to z, =0.0λ A series reactance to z The stub ength is: =0.397λ b=.33 Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 4 Exampe 5.3 Soution Zo b=.33 Zo Zo Z= Z Y Open or shorte stub z= Z=00+j80Ω, Zo=50Ω, fo=ghz. Pot z =+j.6 Draw SWR an z = circes Transform z to z, =0.463λ A series reactance to z The stub ength is: =0.03λ b=.33 Dr. W.J.R. Hoefer Dr. Wofgang J.R. Hoefer EEC 454 Microwave Engineering =0.03λ 5 8
Singe-stub series matching on Smith Chart +jx circe Z z = 00 + j80ω = + j.6 = 0.38 0.08 = 0.0λ = 0.5 0.08 + 0.7 = 0.463λ z z = = + j.33 j.33 = 0.397λ = 0.03λ Dr. Y. Baeyens E438-Microwave Circuit Design.5 36/5
Two soutions singe-stub series matching engths for both soutions approx. simiar, so no big ifference in banwith Series matching not so convenient, requires seperate connection to conuctor an groun Anaytica soution: see Pozar p.34-35 Dr. Y. Baeyens E438-Microwave Circuit Design.5 37/5
Singe-stub tuning Series stubs Smith chart For a oa impeance Z =00+j80, esign two singe-stub series tuning networks to match this oa to a 50Ω ine at GHz. z = + j.6 z =+j.33 z o.c. = (0.38 0.08) = 0.0λ = (0.5 0.08) + 0.7 = 0.463λ -jx =+jx z =-j.33 z z =.00 j.33 =.00 + j.33 = 0.397λ = 0.03λ
Singe-stub tuning At GHz, Z can be moee as a series combination of R=00Ω an =6.37 nh. The frequency response is then = 0.0 λ = 0.463 λ = 0.397 λ = 0.03 λ
Singe-stub tuning Stunt stubs anaytica soution To erive formuas for an, et the oa impeance be written as Z = / Y = R + X. The impeance Z own a ength,, of ine from the oa is where t = tan β. The amittance at this point is thus For matching reason, the (which impies t) is chosen so that G = Y = Z. 0 / 0
Singe-stub tuning This resuts in a quaratic equation for t: Soving for t gives t = X / Z0 for R = Z0 Thus, the two principa soutions for are
Singe-stub tuning For the require stub engths, first use t in (5.8b) to fin the stub susceptance, an B s = -B. Then, for an open-circuit stub, Whie for a short-circuite stub, If the resutant ength is negative, λ/ can be ae to give a positive resut.
Singe-stub tuning Series stubs anaytica soution The input impeance Z in = R in +j X in own a ength from the oa can be first evauate. The matching conition is R in = Z 0 at the stub (et t =tanβ ), t = B / Y 0 for G = Y 0 an the two principa soutions for are then The require stub engths are for an open-circuite stub. for a short-circuite stub. where X was obtaine by substituting t into (5.3b)
Doube Stub Matching Disavantages of Matching with Singe Stub: A variabe ength of ine between the oa an the stub is neee. This wou be a probem if an ajustabe tuner was esire. Soution: Doube stub matching two tuning stubs in fixe positions. Ajustabe stubs are usuay connecte in parae to the main fee ine. Doube stub tuner cannot match a oa impeances. Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 6
Doube Shunt Stub Matching Y o Y Y o Y o jb jb Y o Y Y o Y o Y = Z Open or shorte stub Open or shorte stub Matching Operations Seect, so that y ies on the rotate +jb circe; the amount of rotation is waveengths towars the oa. In practice, =λ/8 or 3λ/8. Transform y towar the generator through a ength ; the new amittance, y =+jb, ies on the +jb circe. Seect, so that the stub susceptance is b. Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 7
Exampe 5.4 Soution Y o Y o Y o Y jb jb Y Y o Y o Shorte stub Shorte stub Z =60 j80ω, Z o =50Ω, =λ/8, f o =GHz. Pot y =0.3+j0.4 Draw conuctance circes y y ; b =.34 y y ; via the SWR circe. y ; b =3.38 Forbien Region Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 8
Microwave Engineering January 9, 003 Exampe 5.4 Soution Yo Yo Yo jb Yo Shorte stub Y jb Y Yo Shorte stub Z=60 j80ω, Zo=50Ω, =λ/8, fo=ghz. Pot y =0.3+j0.4 Draw conuctance circes y y; b=.34 y y; via the SWR circe. y ; b=3.38 Forbien Region Dr. W.J.R. Hoefer EEC 454 Microwave Engineering 8 Exampe 5.4 Soution Yo Yo Yo jb Yo Shorte stub Y jb Y Yo Shorte stub Z=60 j80ω, Zo=50Ω, =λ/8, fo=ghz. Pot y =0.3+j0.4 Draw conuctance circes y y; b= 0.4 y y; via the SWR circe. y ; b=.38 Dr. W.J.R. Hoefer Dr. Wofgang J.R. Hoefer Forbien Region EEC 454 Microwave Engineering 9 0